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numsp384t1

384-bit prime field TwistedEdwards curve.
ax2+y21+dx2y2ax^2 + y^2 \equiv 1 + dx^2y^2

Parameters

NameValue
p0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3
a0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec2
d0x5158a
G(0x08, 0x749cdaba136ce9b65bd4471794aa619daa5c7b4c930bff8ebd798a8ae753c6d72f003860febabad534a4acf5fa7f5bee)
n0x3fffffffffffffffffffffffffffffffffffffffffffffffecd7d11ed5a259a25a13a0458e39f4e451d6d71f70426e25
h0x04


SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec2)
d = K(0x5158a)
E = EllipticCurve(K, (K(-1/48) * (a^2 + 14*a*d + d^2),K(1/864) * (a + d) * (-a^2 + 34*a*d - d^2)))
def to_weierstrass(a, d, x, y):
return ((5*a + a*y - 5*d*y - d)/(12 - 12*y), (a + a*y - d*y -d)/(4*x - 4*x*y))
def to_twistededwards(a, d, u, v):
y = (5*a - 12*u - d)/(-12*u - a + 5*d)
x = (a + a*y - d*y -d)/(4*v - 4*v*y)
return (x, y)
G = E(*to_weierstrass(a, d, K(0x08), K(0x749cdaba136ce9b65bd4471794aa619daa5c7b4c930bff8ebd798a8ae753c6d72f003860febabad534a4acf5fa7f5bee)))
E.set_order(0x3fffffffffffffffffffffffffffffffffffffffffffffffecd7d11ed5a259a25a13a0458e39f4e451d6d71f70426e25 * 0x04)
# This curve is a Weierstrass curve (SAGE does not support TwistedEdwards curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_twistededwards functions to convert the points.
SAGE


JSON

{
"name": "numsp384t1",
"desc": "",
"form": "TwistedEdwards",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec3",
"bits": 384
},
"params": {
"a": {
"raw": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec2"
},
"d": {
"raw": "0x5158a"
}
},
"generator": {
"x": {
"raw": "0x08"
},
"y": {
"raw": "0x749cdaba136ce9b65bd4471794aa619daa5c7b4c930bff8ebd798a8ae753c6d72f003860febabad534a4acf5fa7f5bee"
}
},
"order": "0x3fffffffffffffffffffffffffffffffffffffffffffffffecd7d11ed5a259a25a13a0458e39f4e451d6d71f70426e25",
"cofactor": "0x04"
}

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